Computing quantum Bell inequalities

• Facet Bell inequalities delineate the classical from the quantum, and quantum Bell inequalities separates the quantum from post-quantum world.

• The famous Tsirelson-Landau-Masanes arcsin inequality remains the only known tight quantum Bell inequality (in fact describing a boundary of the quantum correlation set) known since 1987. 

• Can we find new quantum Bell inequalities? It is natural to consider the next nontrivial scenario, two parties three measurements and two outputs, whose quantum correlation set is denoted Cor(3,3) in Tsirelson's paper. Here there must exist a new type of quantum Bell inequality, but I failed at computing its explicit form in this paper.